diff --git a/llvm/lib/IR/ConstantRange.cpp b/llvm/lib/IR/ConstantRange.cpp
--- a/llvm/lib/IR/ConstantRange.cpp
+++ b/llvm/lib/IR/ConstantRange.cpp
@@ -1221,6 +1221,15 @@
   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
     return getEmpty();
 
+  if (const APInt *RHSInt = RHS.getSingleElement()) {
+    // UREM by null is UB.
+    if (RHSInt->isNullValue())
+      return getEmpty();
+    // Use APInt's implementation of UREM for single element ranges.
+    if (const APInt *LHSInt = getSingleElement())
+      return {LHSInt->urem(*RHSInt)};
+  }
+
   // L % R for L < R is L.
   if (getUnsignedMax().ult(RHS.getUnsignedMin()))
     return *this;
@@ -1234,6 +1243,15 @@
   if (isEmptySet() || RHS.isEmptySet())
     return getEmpty();
 
+  if (const APInt *RHSInt = RHS.getSingleElement()) {
+    // SREM by null is UB.
+    if (RHSInt->isNullValue())
+      return getEmpty();
+    // Use APInt's implementation of SREM for single element ranges.
+    if (const APInt *LHSInt = getSingleElement())
+      return {LHSInt->srem(*RHSInt)};
+  }
+
   ConstantRange AbsRHS = RHS.abs();
   APInt MinAbsRHS = AbsRHS.getUnsignedMin();
   APInt MaxAbsRHS = AbsRHS.getUnsignedMax();
diff --git a/llvm/test/Transforms/SCCP/binaryops-range-special-cases.ll b/llvm/test/Transforms/SCCP/binaryops-range-special-cases.ll
--- a/llvm/test/Transforms/SCCP/binaryops-range-special-cases.ll
+++ b/llvm/test/Transforms/SCCP/binaryops-range-special-cases.ll
@@ -98,16 +98,10 @@
 
 define void @urem_cmp_constants() {
 ; CHECK-LABEL: @urem_cmp_constants(
-; CHECK-NEXT:    [[UREM_1:%.*]] = urem i16 12704, 12704
-; CHECK-NEXT:    [[C_1:%.*]] = icmp eq i16 [[UREM_1]], 0
-; CHECK-NEXT:    call void @use(i1 [[C_1]])
-; CHECK-NEXT:    [[C_2:%.*]] = icmp eq i16 [[UREM_1]], 1
-; CHECK-NEXT:    call void @use(i1 [[C_2]])
-; CHECK-NEXT:    [[UREM_2:%.*]] = urem i16 12704, 3
-; CHECK-NEXT:    [[C_3:%.*]] = icmp eq i16 [[UREM_2]], 2
-; CHECK-NEXT:    call void @use(i1 [[C_3]])
-; CHECK-NEXT:    [[C_4:%.*]] = icmp eq i16 [[UREM_2]], 1
-; CHECK-NEXT:    call void @use(i1 [[C_4]])
+; CHECK-NEXT:    call void @use(i1 true)
+; CHECK-NEXT:    call void @use(i1 false)
+; CHECK-NEXT:    call void @use(i1 true)
+; CHECK-NEXT:    call void @use(i1 false)
 ; CHECK-NEXT:    [[UREM_3:%.*]] = urem i16 12704, 0
 ; CHECK-NEXT:    [[C_5:%.*]] = icmp eq i16 [[UREM_3]], 1
 ; CHECK-NEXT:    call void @use(i1 [[C_5]])
@@ -132,16 +126,10 @@
 
 define void @srem_cmp_constants() {
 ; CHECK-LABEL: @srem_cmp_constants(
-; CHECK-NEXT:    [[SREM_1:%.*]] = srem i16 12704, 12704
-; CHECK-NEXT:    [[C_1:%.*]] = icmp eq i16 [[SREM_1]], 0
-; CHECK-NEXT:    call void @use(i1 [[C_1]])
-; CHECK-NEXT:    [[C_2:%.*]] = icmp eq i16 [[SREM_1]], 1
-; CHECK-NEXT:    call void @use(i1 [[C_2]])
-; CHECK-NEXT:    [[SREM_2:%.*]] = srem i16 12704, 3
-; CHECK-NEXT:    [[C_3:%.*]] = icmp eq i16 [[SREM_2]], 2
-; CHECK-NEXT:    call void @use(i1 [[C_3]])
-; CHECK-NEXT:    [[C_4:%.*]] = icmp eq i16 [[SREM_2]], 1
-; CHECK-NEXT:    call void @use(i1 [[C_4]])
+; CHECK-NEXT:    call void @use(i1 true)
+; CHECK-NEXT:    call void @use(i1 false)
+; CHECK-NEXT:    call void @use(i1 true)
+; CHECK-NEXT:    call void @use(i1 false)
 ; CHECK-NEXT:    [[SREM_3:%.*]] = srem i16 12704, 0
 ; CHECK-NEXT:    [[C_5:%.*]] = icmp eq i16 [[SREM_3]], 1
 ; CHECK-NEXT:    call void @use(i1 [[C_5]])